Equation 677 Database

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Magma f5a4b9b1928c…

magma f5a4b9b1928c
Size
336
Isomorphism class hash
f5a4b9b1928c8951b71955184b98e820719df9d1d61aafbc27d16b94d1e65b03
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 335) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 16:25:51
Display reorder
92,93,94,95,96,97,98,99,100,101,102,88,89,90,91,326,247,286,252,249,203,17,0,204,18,1,205,19,2,206,20,3,207,21,4,208,253,250,287,254,5,198,11,6,199,12,7,200,13,8,201,14,9,202,15,10,284,251,248,285,16,40,32,33,34,35,36,37,38,39,41,42,295,292,293,294,322,325,319,334,308,298,303,309,43,115,180,44,116,181,45,117,182,46,118,183,47,119,184,48,120,185,49,121,186,50,122,175,296,304,307,297,123,176,51,124,177,52,125,178,53,126,179,54,127,209,212,213,214,215,216,217,218,219,230,232,234,210,211,229,315,332,316,317,79,110,75,80,111,76,77,112,260,268,267,261,81,113,66,82,269,258,263,265,67,83,103,68,84,104,69,85,105,70,86,106,71,87,107,72,264,266,259,262,108,73,78,109,74,64,56,57,58,59,60,61,62,63,65,55,299,300,301,302,329,333,328,330,305,291,310,306,27,187,173,22,188,174,114,189,280,255,281,278,28,190,165,29,191,166,30,192,167,31,193,168,256,282,279,257,194,169,24,195,170,25,196,171,26,197,172,23,283,290,288,289,221,222,223,224,225,226,228,231,233,235,220,227,320,323,331,324,157,143,133,158,144,134,159,145,135,160,146,136,161,147,137,162,148,138,163,149,139,164,150,140,275,272,270,276,273,271,277,274,128,153,151,129,154,152,130,155,141,131,156,142,132,237,238,239,240,241,242,243,244,245,246,236,313,314,312,311,327,318,321,335 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 336 = 16 + 5*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#0998765ec1482be10f1d3ba0fd5c4e73adbfa919f225aca7155f0867dcd51bc9, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 76} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-07 16:25:52 · history